Felix Berezin: Life and death of the mastermind of supermathematics

M. Shifman9789812705334, 9812705333, 9812705325, 9789812705327, 9789812770486

Felix Berezin was an outstanding Soviet mathematician who in the 1960s and 70s was the driving force behind the emergence of the branch of mathematics now known as supermathematics. The integral over the anticommuting Grassmann variables that he introduced in the 1960s laid the foundation for the path integral formulation of quantum field theory with fermions, the heart of modern supersymmetric field theories and superstrings. The Berezin integral is named for him, as is the closely related construction of the Berezinian, which may be regarded as the superanalog of the determinant. This book features a masterfully written memoir by Berezin’s widow, Elena Karpel, who narrates a remarkable account of Berezin’s life and his struggle for survival under the totalitarian Soviet regime. Supplemented with recollections by his close friends and colleagues, Berezin’s accomplishments in mathematics, his novel ideas and breakthrough works, are reviewed in two articles written by Andrei Losev and Robert Minlos.

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Table of contents :
CONTENTS……Page 9
Foreword M. Shifman……Page 3
General acknowledgments……Page 6
Additional acknowledgments……Page 7
List of contributors……Page 8
Part I……Page 11
1.1. Mathematical physics as a style of theoretical physics……Page 12
1.2. Outline of the paper……Page 14
2.1. Geometry, algebra and supergeometry – an outline……Page 15
2.2. A warm-up exercise: an integral over circle……Page 16
2.3. Definition of the Berezin integral……Page 18
3. Differential forms as functions on the superspace and their integration……Page 19
4. The Hodge star operation as an odd Fourier transform……Page 22
5. The Mathai-Quillen representative and supermanifolds as fractions……Page 23
6. The BV master equation as an odd Fourier transform of the de Rham equation……Page 25
7. An exercise in the BV language……Page 28
8. The BV integral……Page 29
9.1. Symmetric systems in the BV language……Page 30
9.2. Gauge fixing as the BV integral……Page 32
10.1. Differential graded Lie algebras and homotopical Lie algebras……Page 33
10.3. Higher terms in antifields and a new notion of symmetry……Page 34
11. Instead of conclusion: Dreams on a BV M-theory……Page 36
Appendix: Books by F.A. Berezin……Page 37
References……Page 39
1. What He Achieved in Science……Page 40
2. Early Years……Page 42
3. The First Period of Work at the University……Page 43
4. The Last Period……Page 49
5. F. A. Berezin’s Social and Political Status and Position at the Department……Page 53
References……Page 60
Part II……Page 62
On a envie de parler … Natalie Berezin……Page 63
The Last Journey. Remembering F.A. Berezin Elena Karpel……Page 64
Beginning of the End……Page 65
Moscow – Krasnoyarsk……Page 68
Krasnoyarsk – Magadan……Page 114
Magadan – Seymchan – Magadan……Page 119
Magadan – Moscow……Page 128
The End and Beginning……Page 138
Remembering Alik Berezin Victor Maslov……Page 158
On Berezin Misha Shubin……Page 161
My Recollections on Berezin Anatoly Vershik……Page 165
About Alik Berezin and Some of His Works. Ten Years Later 161 Anatoly Vershik……Page 170
References……Page 179
Reminiscences of a Close Friend Nikita Vvedenskaya……Page 180
Acquaintance in Absentia……Page 190
How we Wound up in Siberia……Page 191
I Meet Berezin for the First Time……Page 194
A Seminar at the Institute of Physical Problems……Page 197
The Hassle with my Thesis Defense; Berezin is my Opponent……Page 199
Kolyma Stories……Page 203
Novosibirsk 1979, Akademgorodok, Thesis Defense……Page 208
1980 and Later……Page 212
About Alik Berezin and His Time Victor Palamodov……Page 215
Introduction……Page 227
From the history of Berezin’s inequalities……Page 232
References……Page 237
Part III From Felix Berezin’s Archives……Page 238
Letter to Academician R.V. Khokhlov, the Rector of the Moscow State University……Page 239
I . Acceptance of new students……Page 240
II. Admission to the Graduate School……Page 242
III. Administration’s treatment of t h e faculty. Admitting new students……Page 243
IV. Scientific policy……Page 245
Letter to the Governing Board of the Moscow Mathematical Society……Page 250
From Wikipedia……Page 252